TY - JOUR

T1 - Finite-temperature entanglement negativity of free fermions

AU - Shapourian, Hassan

AU - Ryu, Shinsei

N1 - Funding Information:
The authors would like to acknowledge fruitful discussions with E Tonni, Z Zimboras, K Shiozaki, X Wen, T H Hsieh, P Ruggiero, P-Y Chang, D Chowdhury, J Kudler-Flam and M-T Tan. HS would like to thank Pasquale Calabrese for insightful discussions and constructive comments on the results, and for pointing out the previous literature about the generalized Fisher Hartwig conjecture. This work was supported in part by the National Science Foundation under Grant No. DMR-1455296, and under Grant No. NSF PHY-1748958. We are grateful to the KITP Program Quantum Physics of Information (Sep 18 Dec 15, 2017), where some part of the work was performed. We thank the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work. HS acknowledges the support from the ACRI fellowship (Italy) and the KITP graduate fellowship program.

PY - 2019/4/30

Y1 - 2019/4/30

N2 - The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper (Shapourian et al 2017 Phys. Rev. B 95 165101). In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.

AB - The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper (Shapourian et al 2017 Phys. Rev. B 95 165101). In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.

KW - Conformal field theory

KW - Entanglement entropies

KW - Entanglement in extended quantum systems

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U2 - 10.1088/1742-5468/ab11e0

DO - 10.1088/1742-5468/ab11e0

M3 - Article

AN - SCOPUS:85069544132

VL - 2019

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 4

M1 - 43106

ER -